ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simplbi2com Unicode version

Theorem simplbi2com 1374
Description: A deduction eliminating a conjunct, similar to simplbi2 377. (Contributed by Alan Sare, 22-Jul-2012.) (Proof shortened by Wolf Lammen, 10-Nov-2012.)
Hypothesis
Ref Expression
simplbi2com.1  |-  ( ph  <->  ( ps  /\  ch )
)
Assertion
Ref Expression
simplbi2com  |-  ( ch 
->  ( ps  ->  ph )
)

Proof of Theorem simplbi2com
StepHypRef Expression
1 simplbi2com.1 . . 3  |-  ( ph  <->  ( ps  /\  ch )
)
21simplbi2 377 . 2  |-  ( ps 
->  ( ch  ->  ph )
)
32com12 30 1  |-  ( ch 
->  ( ps  ->  ph )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  mo2r  1995  mo3h  1996  elres  4694  xpidtr  4765  peano5nnnn  7172  peano5nni  8161
  Copyright terms: Public domain W3C validator